Detecting triplet locking by triplet synchronization indices

Kralemann, Björn; Pikovsky, Arkady; Rosenblum, Michael

doi:10.1103/physreve.87.052904

Cited by 20 publications

(19 citation statements)

References 46 publications

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“…By a CCD acquisition system, Hu et al confirmed this SS state in experiment [16]. By the same acquisition system, Jia et al successfully generated in experiment the triplet synchronization state predicted theoretically by Kralemann et al [17,18]. When more than three metronomes are coupled, a general phenomenon is that the metronomes can be self-organized into different synchronous clusters.…”

Section: Introductionmentioning

confidence: 82%

Synchronization of coupled metronomes on two layers

Zhang

Wang

2017

Front. Phys.

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Coupled metronomes serve as a paradigmatic model for exploring the collective behaviors of complex dynamical systems, as well as a classical setup for classroom demonstrations of synchronization phenomena. Whereas previous studies of metronome synchronization have been concentrating on symmetric coupling schemes, here we consider the asymmetric case by adopting the scheme of layered metronomes. Specifically, we place two metronomes on each layer, and couple two layers by placing one on top of the other. By varying the initial conditions of the metronomes and adjusting the friction between the two layers, a variety of synchronous patterns are observed in experiment, including the splay synchronization (SS) state, the generalized splay synchronization (GSS) state , the anti-phase synchronization (APS) state, the in-phase delay synchronization (IPDS) state, and the in-phase synchronization (IPS) state. In particular, the IPDS state, in which the metronomes on each layer are synchronized in phase but are of a constant phase delay to metronomes on the other layer, is observed for the first time. In addition, a new technique based on audio signals is proposed for pattern detection, which is more convenient and easier to apply than the existing acquisition techniques. Furthermore, a theoretical model is developed to explain the experimental observations, and is employed to explore the dynamical properties of the patterns, including the basin distributions and the pattern transitions. Our study sheds new lights on the collective behaviors of coupled metronomes, and the developed setup can be used in the classroom for demonstration purposes.Comment: 19 pages, 6 figure

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Section: Introductionmentioning

confidence: 82%

Synchronization of coupled metronomes on two layers

Zhang

Wang

2017

Front. Phys.

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“…The phase decompositions can be applied for pairwise couplings but, more importantly, joint coupling influences can also be inferred. In such cases one can detect unique states characteristic only of the joint couplings, like triplet synchronization [61]. In these kind of analysis, the effective coupling [45,62] should be distinguished by appropriate use of surrogate testing [63].…”

Section: Discussionmentioning

confidence: 99%

A tutorial on time-evolving dynamical Bayesian inference

Stankovski

Duggento

McClintock

et al. 2014

Eur. Phys. J. Spec. Top.

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Abstract. In view of the current availability and variety of measured data, there is an increasing demand for powerful signal processing tools that can cope successfully with the associated problems that often arise when data are being analysed. In practice many of the data-generating systems are not only time-variable, but also influenced by neighbouring systems and subject to random fluctuations (noise) from their environments. To encompass problems of this kind, we present a tutorial about the dynamical Bayesian inference of time-evolving coupled systems in the presence of noise. It includes the necessary theoretical description and the algorithms for its implementation. For general programming purposes, a pseudocode description is also given. Examples based on coupled phase and limit-cycle oscillators illustrate the salient features of phase dynamics inference. State domain inference is illustrated with an example of coupled chaotic oscillators. The applicability of the latter example to secure communications based on the modulation of coupling functions is outlined. MatLab codes for implementation of the method, as well as for the explicit examples, accompany the tutorial.

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“…As discussed below, reconstruction is not possible if oscillators synchronize. Practically, in order to exclude from the consideration the synchronous states, we compute pairwise and triplet synchronization indices [51] according to…”

Section: General Approachmentioning

confidence: 99%

Reconstructing effective phase connectivity of oscillator networks from observations

2014

Self Cite

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We present a novel approach for recovery of the directional connectivity of a small oscillator network by means of the phase dynamics reconstruction from multivariate time series data. The main idea is to use a triplet analysis instead of the traditional pairwise one. Our technique reveals an effective phase connectivity which is generally not equivalent to a structural one. We demonstrate that by comparing the coupling functions from all possible triplets of oscillators, we are able to achieve in the reconstruction a good separation between existing and non-existing connections, and thus reliably reproduce the network structure.

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Detecting triplet locking by triplet synchronization indices

Cited by 20 publications

References 46 publications

Synchronization of coupled metronomes on two layers

Synchronization of coupled metronomes on two layers

A tutorial on time-evolving dynamical Bayesian inference

Reconstructing effective phase connectivity of oscillator networks from observations

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